Exponential convergence of hp-ILGFEM for semilinear elliptic boundary value problems with monomial reaction
Year: 2025
Type: other
Abstract: We study the fully explicit numerical approximation of a semilinear elliptic boundary value model problem, which features a monomial reaction and analytic forcing, in a bounded polygon Ω ⊂ R² with a finite number of straight edges. In particular, we analyse the convergence of hp-type iterative linearized Galerkin (hp-ILG) solvers. Our convergence analysis is carried out for conforming hp-finite element (FE) Galerkin discretizations on sequences of regular, simplicial partitions of Ω, with geometric corner refinement, with polynomial degrees increasing in tandem with the geometric mesh refinement towards the corners of Ω. For a sequence of discrete solutions generated by the ILG solver with a stopping criterion that is consistent with the exponential convergence of the exact hp-FE Galerkin solution, we prove exponential convergence in H¹(Ω) to the unique weak solution of the boundary value problem. Numerical experiments illustrate the exponential convergence of the numerical approximations obtained from the proposed scheme in terms of the number of degrees of freedom as well as of the computational complexity involved.
Source: ETH Zürich Research Collection
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6966240696
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